Finite Group Databasebeta

← #15638548

Subgroups — #15638548

Order 2816.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4339C211yesmaximal, characteristic, complemented
2#13080560C211yesmaximal, characteristic, complemented
3#13080538C211yesmaximal, characteristic, complemented
4#13080512C212yesmaximal, complemented
5#13080486C211yesmaximal, characteristic, complemented
6#13080460C212yesmaximal, complemented
7#13080434C211yesmaximal, characteristic, complemented
8#13080372C211yesmaximal, characteristic, complemented
9#13080346C211yesmaximal, characteristic, complemented
10#13080319C212yesmaximal, complemented
11D4×#4324C211yesmaximal, characteristic, complemented
12#13080297C212yesmaximal, complemented
13D4×#4323C211yesmaximal, characteristic, complemented
14#13079588C211yesmaximal, characteristic, complemented
15#13079545C211yesmaximal, characteristic, complemented
16#13079404C212yesmaximal, complemented
17#13079381C212yesmaximal, complemented
18#13078670C211yesmaximal, characteristic, complemented
19#13078628C211yesmaximal, characteristic, complemented
20#13077832C212yesmaximal, complemented
21C2×#10622650C212yesmaximal, complemented
22#13077640C211yesmaximal, characteristic, complemented
23C11×#3519C211yesmaximal, characteristic, complemented
24C22×#4339C2212yescomplemented
25C11×#555C2211yescharacteristic, complemented
26C11×#554C2211yescharacteristic
27C11×#553—21no—
28C11×#553C2212yescomplemented
29C11×#550C2211yescharacteristic, complemented
30C11×#546—22no—
31C11×#546C2212yescomplemented
32D42×C11—21no—
33D42×C11C2211yescharacteristic
34C11×#540—21no—
35C11×#538—22no—
36C11×#532C2211yescharacteristic, complemented
37C11×#529C2211yescharacteristic, complemented
38C11×#525C2212yescomplemented
39C2×C11×#121C2212yescomplemented
40C11×#518—21no—
41C2×C4×D4×C11C2211yescharacteristic
42C2×#67003C2212yescomplemented
43C2×#67003C2212yescomplemented
44D4×C22⋊D11—21no—
45C22×#4324C2212yescomplemented
46C22×#4323C2212yescomplemented
47#10623322C2212yescomplemented
48#10623084C2211yescharacteristic, complemented
49#10623083C2212yescomplemented
50#10623082C2211yescharacteristic, complemented
51#10623081C2212yescomplemented
52D4×D44C2211yescharacteristic
53#10623079—21no—
54#10623078—22no—
55C4×D4×D11—21no—
56D4×Dic22C2211yescharacteristic
57#10623038—21no—
58#10623021—22no—
59#10623008C2211yescharacteristic, complemented
60C4×#4339C2211yescharacteristic, complemented
61#10622852C2212yescomplemented
62#10622851C2212yescomplemented
63#10622831C2212yescomplemented
64#10622830C2212yescomplemented
65C2×C22⋊(C11⋊C8)C2212yescomplemented
66C2×C22⋊(C11⋊C8)C2212yescomplemented
67#10622706C2211yescharacteristic, complemented
68#10622704C2211yescharacteristic, complemented
69#10622701C2211yescharacteristic, complemented
70#10622697C2211yescharacteristic, complemented
71#10622689C2211yescharacteristic, complemented
72#10622688C2211yescharacteristic, complemented
73#10622686C2211yescharacteristic, complemented
74#10622685C2211yescharacteristic, complemented
75#10622681C2212yescomplemented
76#10622679C2211yescharacteristic, complemented
77#10622676C2211yescharacteristic, complemented
78#10622672C2212yescomplemented
79#10622670C2211yescharacteristic, complemented
80#10622667C2211yescharacteristic, complemented
81#10622664C2212yescomplemented
82#10622663C2212yescomplemented
83#10622661C2212yescomplemented
84#10622660C2212yescomplemented
85#10622660C2211yescharacteristic, complemented
86#10622659C2212yescomplemented
87#10622658C2211yescharacteristic, complemented
88#10622654C2212yescomplemented
89#10622654C2212yescomplemented
90#10622654C2212yescomplemented
91#10622653C2212yescomplemented
92#10622651C2212yescomplemented
93#10622651C2212yescomplemented
94#10622651C2212yescomplemented
95#10622650C2211yescharacteristic
96#10622650C2212yescomplemented
97#10622650C2212yescomplemented
98#10622650C2212yescomplemented
99#10622650C2212yescomplemented
100#10622650C2212yescomplemented
101#10622650C2212yescomplemented
102#10622650C2212yescomplemented
103#10622650C2212yescomplemented
104#10622649C2212yescomplemented
105#10622648C2211yescharacteristic, complemented
106#10622648C2212yescomplemented
107#10622644C2211yescharacteristic, complemented
108C4×#4326C2211yescharacteristic, complemented
109#10622640C2211yescharacteristic, complemented
110C4×#4325C2211yescharacteristic, complemented
111#10622632C2211yescharacteristic, complemented
112C4×#4324C2211yescharacteristic, complemented
113C4×#4324C2212yescomplemented
114#10622629C2212yescomplemented
115#10622629C2212yescomplemented
116#10622628C2211yescharacteristic, complemented
117C4×#4323C2211yescharacteristic, complemented
118C4×#4323C2212yescomplemented
119D4×C11⋊C8C2211yescharacteristic
120D4×C11⋊C8C2211yescharacteristic
121D4×C11⋊C8C2211yescharacteristic, complemented
122D4×C11⋊C8C2211yescharacteristic, complemented
123D4×C11⋊C8C2212yescomplemented
124D4×C11⋊C8C2212yescomplemented
125#10622616C2212yescomplemented
126#10622615C2212yescomplemented
127#10622615C2212yescomplemented
128#10622609C2212yescomplemented
129#10622583C2212yescomplemented
130C2×#66874C2212yescomplemented
131#10622581C2212yescomplemented
132C2×#66873C2212yescomplemented
133#10622538C2211yescharacteristic, complemented
134#10622538C2211yescharacteristic, complemented
135C2×C11×#41—21no—
136C2×C11×#41C2312yes—
137C22×D4×C11—22no—
138C22×D4×C11—21no—
139C22×D4×C11D411yescharacteristic
140C22×D4×C11C2312yes—
141C23×C4×C11C2312yes—
142C22×C22⋊D11—22no—
143C2×D4×D11—21no—
144C2×#4339—22no—
145C2×#4339—22no—
146C2×#4339—44no—
147C2×#4339—44no—
148C2×#4339C2311yescharacteristic
149C2×#4339C2312yes—
150C2×#4339C2312yes—
151C2×#4339C2312yes—
152C22×D44C2312yes—
153C22×C4×D11—22no—
154C22×Dic22C2312yes—
155C11×C4⋊Q8C2311yescharacteristic
156C11×#127—21no—
157C11×#127C2311yescharacteristic
158C11×#126—22no—
159C11×#126—21no—
160C11×#125—21no—
161C11×#125C2311yescharacteristic
162C11×#124—22no—
163C11×#124—21no—
164C11×#124C2311yescharacteristic
165C11×#123—22no—
166C11×#123—21no—
167C11×#123—22no—
168C11×#123—22no—
169C11×C22⋊Q8—22no—
170C11×C22⋊Q8C2311yescharacteristic
171C11×C22⋊Q8C2312yes—
172C11×#121—22no—
173C11×#121—21no—
174C11×#121—22no—
175C11×#121—22no—
176C11×#121—21no—
177C11×#121—21no—
178C11×#121—22no—
179C11×#121—22no—
180C11×#121C2311yescharacteristic
181C11×#121C2312yes—
182C11×#121C2312yes—
183C11×#121C2312yes—
184C11×#121C2312yes—
185C11×#120—22no—
186C11×#120—22no—
187C11×#120—22no—
188C4×Q8×C11C2311yescharacteristic
189C4×D4×C11—21no—
190C4×D4×C11—22no—
191C4×D4×C11—22no—
192C4×D4×C11—21no—
193C4×D4×C11—21no—
194C4×D4×C11—22no—
195C4×D4×C11—21no—
196C4×D4×C11D411yescharacteristic
197C4×D4×C11D412yes—
198C4×D4×C11D411yescharacteristic
199C4×D4×C11C2311yescharacteristic
200C4×D4×C11C2312yes—
201C4×D4×C11C2311yescharacteristic
202C4×D4×C11C2312yes—
203C4×D4×C11C2311yescharacteristic
204C11×#117—21no—
205C11×#117—21no—
206C11×#117C2312yes—
207C2×C11×C4⋊C4D411yescharacteristic
208C2×C11×C4⋊C4C2312yes—
209C2×C11×C22⋊C4—22no—
210C2×C11×C22⋊C4—22no—
211C2×C11×C22⋊C4D412yes—
212C2×C42×C11C2311yescharacteristic
213#67006—22no—
214#67003—44no—
215#67003—44no—
216C2×#4326C2311yescharacteristic
217C2×#4326C2312yes—
218C2×#4325C2311yescharacteristic
219C2×#4325C2312yes—
220#66993—21no—
221#66992—22no—
222#66991—21no—
223#66990—22no—
224D4×Dic11—21no—
225C2×#4324—44no—
226C2×#4324C2311yescharacteristic
227C2×#4324C2312yes—
228C2×#4324C2312yes—
229C2×#4324C2312yes—
230C2×#4324C2312yes—
231C2×#4323—44no—
232C2×#4323C2311yescharacteristic
233C2×#4323C2312yes—
234C2×#4323C2312yes—
235C2×#4323C2312yes—
236C2×#4323C2312yes—
237#66983—21no—
238#66983—21no—
239#66983C2312yes—
240#66983C2312yes—
241#66982—22no—
242C4×C22⋊D11—21no—
243C4×C22⋊D11—21no—
244C4×C22⋊D11—22no—
245C4×C22⋊D11—22no—
246#66979C2311yescharacteristic
247#66977C2312yes—
248#66977C2312yes—
249C22×C11⋊C8C2312yes—
250C22×C11⋊C8C2312yes—
251C22×C11⋊C8C2312yes—
252C22×C11⋊C8C2312yes—
253#66949—22no—
254#66948—21no—
255#66947—22no—
256#66946—21no—
257C4⋊C4×D11—21no—
258#66941—21no—
259#66938—22no—
260#66937—22no—
261#66937—22no—
262#66936—22no—
263#66935—22no—
264(C22⋊D11)⋊C4—22no—
265C22⋊C4×D11—22no—
266#66931—22no—
267#66928C2312yes—
268#66927C2311yescharacteristic
269C4×D44—21no—
270C4×D44—21no—
271C4×D44C2311yescharacteristic
272C4×D44C2311yescharacteristic
273#66925—21no—
274C42×D11—21no—
275#66922C2311yescharacteristic
276C4×Dic22C2311yescharacteristic
277C4×Dic22C2311yescharacteristic
278#66899C2311yescharacteristic
279#66899C2311yescharacteristic
280#66896C2311yescharacteristic
281#66896C2312yes—
282#66896C2311yescharacteristic
283#66896C2312yes—
284C22⋊(C11⋊C8)C2312yes—
285C22⋊(C11⋊C8)C2311yescharacteristic
286C22⋊(C11⋊C8)C2311yescharacteristic
287C22⋊(C11⋊C8)C2312yes—
288C22⋊(C11⋊C8)C2312yes—
289C22⋊(C11⋊C8)C2312yes—
290C22⋊(C11⋊C8)C2312yes—
291#66874C2311yescharacteristic
292#66874C2312yes—
293#66874C2312yes—
294#66874C2312yes—
295#66874C2312yes—
296#66874C2312yes—
297#66874C2311yescharacteristic
298#66873C2311yescharacteristic
299#66873C2312yes—
300#66873C2312yes—
301#66873C2312yes—
302#66873C2312yes—
303#66873C2311yescharacteristic
304#66873C2312yes—
305#66872C2311yescharacteristic
306#66872C2312yes—
307#66872C2311yescharacteristic
308#66871C2311yescharacteristic
309#66871C2312yes—
310#66871C2311yescharacteristic
311C4⋊(C11⋊C8)C2311yescharacteristic
312C4⋊(C11⋊C8)C2311yescharacteristic
313C4⋊(C11⋊C8)C2311yescharacteristic
314C4⋊(C11⋊C8)C2311yescharacteristic
315C4×C11⋊C8C2311yescharacteristic
316C4×C11⋊C8C2311yescharacteristic
317C4×C11⋊C8C2312yes—
318#61567—111nomaximal, Sylow
319C24×C11—22no—
320C24×C11C2×D412yes—
321C23×D11—22no—
322C11×#41—42no—
323C11×#41—42no—
324C11×#41—82no—
325C2×Q8×C11—21no—
326C2×Q8×C11C2411yescharacteristic
327C2×D4×C11—24no—
328C2×D4×C11—22no—
329C2×D4×C11—22no—
330C2×D4×C11—21no—
331C2×D4×C11—22no—
332C2×D4×C11—22no—
333C2×D4×C11—22no—
334C2×D4×C11—21no—
335C2×D4×C11—21no—
336C2×D4×C11—22no—
337C2×D4×C11—42no—
338C2×D4×C11—42no—
339C2×D4×C11—44no—
340C2×D4×C11—84no—
341C2×D4×C11C2×D412yes—
342C2×D4×C11C2×D411yescharacteristic
343C2×D4×C11C2×D411yescharacteristic
344C2×D4×C11C2411yescharacteristic
345C2×D4×C11C2412yes—
346C22×C4×C11—22no—
347C22×C4×C11—21no—
348C22×C4×C11—22no—
349C22×C4×C11—22no—
350C22×C4×C11—42no—
351C22×C4×C11—42no—
352C22×C4×C11C2×D411yescharacteristic
353C22×C4×C11C2×D411yescharacteristic
354C22×C4×C11C2×D412yes—
355C22×C4×C11C2×D412yes—
356C22×C4×C11C2×D412yes—
357C22×C4×C11C2411yescharacteristic
358C22×C4×C11C2412yes—
359C22×C4×C11C2412yes—
360C2×C22⋊D11—21no—
361C2×C22⋊D11—22no—
362C2×C22⋊D11—22no—
363C2×C22⋊D11—22no—
364C2×C22⋊D11—22no—
365C2×C22⋊D11—22no—
366C2×C22⋊D11—48no—
367C22×Dic11—22no—
368D4×D11—44no—
369#4339—22no—
370#4339—24no—
371#4339—22no—
372#4339—24no—
373#4339—42no—
374#4339—42no—
375#4339—42no—
376#4339—42no—
377#4339—48no—
378#4339—48no—
379C2×D44—24no—
380C2×D44—21no—
381C2×D44—22no—
382C2×D44—21no—
383C2×D44—42no—
384C2×D44C2412yes—
385C2×D44C2411yescharacteristic
386C2×C4×D11—21no—
387C2×C4×D11—21no—
388C2×C4×D11—22no—
389C2×C4×D11—22no—
390C2×C4×D11—22no—
391C2×C4×D11—21no—
392C2×C4×D11—48no—
393C2×Dic22—24no—
394C2×Dic22—22no—
395C2×Dic22—42no—
396C2×Dic22C2412yes—
397C2×Dic22C2411yescharacteristic
398C11×C4⋊C4—22no—
399C11×C4⋊C4—21no—
400C11×C4⋊C4—21no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—21no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—21no—
405C11×C4⋊C4C2×D411yescharacteristic
406C11×C4⋊C4C2×D411yescharacteristic
407C11×C4⋊C4C2×D412yes—
408C11×C4⋊C4C2411yescharacteristic
409C11×C4⋊C4C2412yes—
410C11×C4⋊C4C2411yescharacteristic
411C11×C22⋊C4—22no—
412C11×C22⋊C4—22no—
413C11×C22⋊C4—21no—
414C11×C22⋊C4—21no—
415C11×C22⋊C4—21no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—21no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—21no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4C2×D412yes—
424C11×C22⋊C4C2×D412yes—
425C11×C22⋊C4C2×D412yes—
426C11×C22⋊C4C2×D412yes—
427C42×C11—22no—
428C42×C11—21no—
429C42×C11C2×D411yescharacteristic
430C42×C11C2×D411yescharacteristic
431C42×C11C2411yescharacteristic
432C42×C11C2411yescharacteristic
433C22⋊Dic11—22no—
434C22⋊Dic11—22no—
435C22⋊Dic11—21no—
436#4326—22no—
437#4326—42no—
438#4325—22no—
439#4325—42no—
440#4324—22no—
441#4324—24no—
442#4324—42no—
443#4324—42no—
444#4324—42no—
445#4323—22no—
446#4323—24no—
447#4323—42no—
448#4323—42no—
449#4323—42no—
450(C2×D11)⋊C4—21no—
451(C2×D11)⋊C4—21no—
452(C2×D11)⋊C4—22no—
453(C2×D11)⋊C4—22no—
454(C2×D11)⋊C4—22no—
455(C2×D11)⋊C4—22no—
456C4⋊Dic11—21no—
457C4⋊Dic11—21no—
458C4⋊Dic11C2411yescharacteristic
459C4⋊Dic11C2411yescharacteristic
460Dic11⋊C4—21no—
461Dic11⋊C4—21no—
462Dic11⋊C4—22no—
463Dic11⋊C4—22no—
464C4×Dic11—21no—
465C4×Dic11—21no—
466C4×Dic11—21no—
467C2×C11⋊C8—42no—
468C2×C11⋊C8—42no—
469C2×C11⋊C8—42no—
470C2×C11⋊C8—42no—
471C2×C11⋊C8C2412yes—
472C2×C11⋊C8C2411yescharacteristic
473C2×C11⋊C8C2411yescharacteristic
474C2×C11⋊C8C2411yescharacteristic
475C2×C11⋊C8C2412yes—
476C2×C11⋊C8C2411yescharacteristic
477#3519D1111yescharacteristic, complemented
478D4×#41—111no—
479#3305—111no—
480#3303—111no—
481#3301—112no—
482#3299—111no—
483#3297—112no—
484#3295—111no—
485#3287—111no—
486#3284—111no—
487#3282—112no—
488D4×SD16—111no—
489#3280—112no—
490D4×D8—111no—
491#3212—111no—
492#3207—111no—
493#3191—112no—
494#3188—112no—
495#3106—111no—
496#3102—111no—
497#3002—112no—
498C2×#449—112no—
499#2972—111no—
500C23×C11—24no—
501C23×C11—21no—
502C23×C11—22no—
503C23×C11—42no—
504C23×C11—42no—
505C23×C11—44no—
506C23×C11—82no—
507C23×C11—82no—
508C23×C11C22×D412yes—
509C23×C11C22×D411yescharacteristic
510C23×C11C22×D412yes—
511C22×D11—21no—
512C22×D11—22no—
513C22×D11—44no—
514C22×D11—44no—
515C22×D11—82no—
516Q8×C11—21no—
517Q8×C11—21no—
518Q8×C11—81no—
519D4×C11—24no—
520D4×C11—22no—
521D4×C11—21no—
522D4×C11—22no—
523D4×C11—22no—
524D4×C11—21no—
525D4×C11—42no—
526D4×C11—44no—
527D4×C11—44no—
528D4×C11—42no—
529D4×C11—82no—
530D4×C11—81no—
531D4×C11—82no—
532D4×C11—82no—
533D4×C11—82no—
534D4×C11#13514yescomplemented
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—22no—
539C2×C4×C11—22no—
540C2×C4×C11—21no—
541C2×C4×C11—21no—
542C2×C4×C11—21no—
543C2×C4×C11—21no—
544C2×C4×C11—22no—
545C2×C4×C11—21no—
546C2×C4×C11—42no—
547C2×C4×C11—42no—
548C2×C4×C11—42no—
549C2×C4×C11—41no—
550C2×C4×C11—42no—
551C2×C4×C11—82no—
552C2×C4×C11—82no—
553C2×C4×C11—82no—
554C2×C4×C11C22×D411yescharacteristic
555C2×C4×C11C22×D411yescharacteristic
556C2×C4×C11C22×D411yescharacteristic
557C2×C4×C11C22×D411yescharacteristic
558C2×C4×C11C22×D412yes—
559C2×C4×C11C22×D412yes—
560C2×C4×C11C22×D411yescharacteristic
561C2×C4×C11C2511yescharacteristic
562C22⋊D11—24no—
563C22⋊D11—44no—
564C22⋊D11—44no—
565C22⋊D11—44no—
566C22⋊D11—44no—
567C22⋊D11—82no—
568C2×Dic11—21no—
569C2×Dic11—21no—
570C2×Dic11—21no—
571C2×Dic11—22no—
572C2×Dic11—44no—
573D44—21no—
574D44—22no—
575D44—22no—
576D44—44no—
577D44—42no—
578D44—81no—
579D44H(5,𝔽2)12yes—
580C4×D11—24no—
581C4×D11—44no—
582C4×D11—44no—
583C4×D11—44no—
584C4×D11—42no—
585C4×D11—81no—
586Dic22—21no—
587Dic22—22no—
588Dic22—22no—
589Dic22—44no—
590Dic22H(5,𝔽2)12yes—
591C11⋊C8—21no—
592C11⋊C8—22no—
593C11⋊C8—21no—
594C11⋊C8—21no—
595C11⋊C8—22no—
596C11⋊C8—21no—
597C22×#41—112no—
598C2×#135—112no—
599C2×#135—112no—
600C22×SD16—112no—
601C22×D8—112no—
602#555C2×D1111yescharacteristic, complemented
603#554C2×D1111yescharacteristic
604#553—21no—
605#553C2×D1112yescomplemented
606#550—111no—
607#550C2×D1111yescharacteristic, complemented
608D4×Q8—111no—
609#548—112no—
610#547—111no—
611#547—221no—
612#546—22no—
613#546—112no—
614#546—222no—
615#546C2×D1112yescomplemented
616D42—21no—
617D42—111no—
618D42—221no—
619D42C2×D1111yescharacteristic
620#540—21no—
621#538—22no—
622#532—111no—
623#532—221no—
624#532C2×D1111yescharacteristic, complemented
625#529C2×D1111yescharacteristic, complemented
626#525—112no—
627#525—222no—
628#525C2×D1112yescomplemented
629C2×#121C2×D1112yescomplemented
630#518—21no—
631C4×#41—111no—
632C2×C4×D4—221no—
633C2×C4×D4C2×D1111yescharacteristic
634#495—112no—
635#493—111no—
636#492—111no—
637#488—112no—
638#487—111no—
639#486—111no—
640#485—111no—
641#485—112no—
642#484—112no—
643#482—111no—
644#482—112no—
645#482—112no—
646#481—112no—
647#479—111no—
648#478—111no—
649#477—111no—
650#476—111no—
651#467—112no—
652#466—112no—
653#466—112no—
654#466—112no—
655#465—112no—
656#465—112no—
657#465—112no—
658#465—112no—
659#464—111no—
660#463—111no—
661#463—112no—
662#463—112no—
663#462—111no—
664#461—111no—
665#460—111no—
666#460—111no—
667#459—111no—
668#459—111no—
669#452—112no—
670#452—111no—
671#452—112no—
672#451—112no—
673#450—112no—
674#450—112no—
675#449—112no—
676#449—111no—
677#449—112no—
678#449—112no—
679#449—112no—
680#449—112no—
681#449—112no—
682#449—112no—
683#449—112no—
684#449—112no—
685#448—112no—
686#447—112no—
687#447—112no—
688C4×Q16—111no—
689C4×SD16—111no—
690C4×SD16—111no—
691C4×SD16—112no—
692C4×D8—111no—
693C4×D8—112no—
694C8×D4—111no—
695C8×D4—111no—
696C8×D4—112no—
697C8×D4—112no—
698C8×D4—111no—
699C8×D4—111no—
700#431—111no—
701#431—111no—
702#416—112no—
703#416—112no—
704C2×#103—112no—
705C2×#102—112no—
706C2×C22⋊C8—112no—
707C2×C22⋊C8—112no—
708C22×C11—22no—
709C22×C11—22no—
710C22×C11—21no—
711C22×C11—22no—
712C22×C11—21no—
713C22×C11—22no—
714C22×C11—21no—
715C22×C11—22no—
716C22×C11—42no—
717C22×C11—41no—
718C22×C11—42no—
719C22×C11—41no—
720C22×C11—41no—
721C22×C11—42no—
722C22×C11—84no—
723C22×C11—164no—
724C22×C11C2×#13514yes—
725C22×C11C23×D411yescharacteristic
726C2×D11—22no—
727C2×D11—41no—
728C2×D11—41no—
729C2×D11—42no—
730C2×D11—42no—
731C2×D11—42no—
732C2×D11—88no—
733C4×C11—21no—
734C4×C11—21no—
735C4×C11—21no—
736C4×C11—22no—
737C4×C11—22no—
738C4×C11—21no—
739C4×C11—41no—
740C4×C11—42no—
741C4×C11—41no—
742C4×C11—41no—
743C4×C11C2×#13512yes—
744C4×C11C2×H(5,𝔽2)11yescharacteristic
745C4×C11C2×H(5,𝔽2)11yescharacteristic
746Dic11—22no—
747Dic11—41no—
748Dic11—42no—
749Dic11—41no—
750C2×#41—21no—
751C2×#41—111no—
752C2×#41—112no—
753C2×#41—112no—
754C2×#41—112no—
755C2×#41—222no—
756C2×#41—222no—
757C2×#41—444no—
758C2×#41—444no—
759C2×#41C22×D1112yes—
760C22×Q8—112no—
761C22×D4—22no—
762C22×D4—21no—
763C22×D4—112no—
764C22×D4—222no—
765C22×D4—221no—
766C22×D4C22⋊D1111yescharacteristic
767C22×D4C22×D1112yes—
768C23×C4—222no—
769C23×C4C22×D1112yes—
770#135—444no—
771#135—444no—
772C2×Q16—111no—
773C2×Q16—112no—
774C2×SD16—111no—
775C2×SD16—111no—
776C2×SD16—112no—
777C2×SD16—112no—
778C2×SD16—112no—
779C2×SD16—112no—
780C2×SD16—112no—
781C2×SD16—444no—
782C2×D8—111no—
783C2×D8—112no—
784C2×D8—112no—
785C2×D8—112no—
786C2×D8—112no—
787C2×D8—444no—
788C22×C8—112no—
789C22×C8—112no—
790C22×C8—112no—
791C22×C8—112no—
792C4⋊Q8—111no—
793C4⋊Q8—221no—
794C4⋊Q8C22×D1111yescharacteristic
795#127—21no—
796#127—111no—
797#127—221no—
798#127C22×D1111yescharacteristic
799#126—22no—
800#126—21no—
801#125—21no—
802#125C22×D1111yescharacteristic
803#124—22no—
804#124—21no—
805#124—112no—
806#124—222no—
807#124C22×D1111yescharacteristic
808#123—22no—
809#123—21no—
810#123—22no—
811#123—22no—
812#123—222no—
813#123—222no—
814#123—222no—
815C22⋊Q8—22no—
816C22⋊Q8—112no—
817C22⋊Q8—112no—
818C22⋊Q8—222no—
819C22⋊Q8—222no—
820C22⋊Q8C22×D1111yescharacteristic
821C22⋊Q8C22×D1112yes—
822#121—22no—
823#121—21no—
824#121—22no—
825#121—22no—
826#121—21no—
827#121—21no—
828#121—22no—
829#121—22no—
830#121—112no—
831#121—112no—
832#121—222no—
833#121—221no—
834#121—221no—
835#121—221no—
836#121—221no—
837#121—222no—
838#121—222no—
839#121C22×D1111yescharacteristic
840#121C22×D1112yes—
841#121C22×D1112yes—
842#121C22×D1112yes—
843#121C22×D1112yes—
844#120—22no—
845#120—22no—
846#120—22no—
847#120—222no—
848#120—222no—
849#120—222no—
850C4×Q8—111no—
851C4×Q8—111no—
852C4×Q8C22×D1111yescharacteristic
853C4×D4—21no—
854C4×D4—22no—
855C4×D4—22no—
856C4×D4—21no—
857C4×D4—21no—
858C4×D4—22no—
859C4×D4—21no—
860C4×D4—111no—
861C4×D4—111no—
862C4×D4—221no—
863C4×D4—222no—
864C4×D4—221no—
865C4×D4—221no—
866C4×D4—222no—
867C4×D4—221no—
868C4×D4—222no—
869C4×D4—221no—
870C4×D4—221no—
871C4×D4C22⋊D1111yescharacteristic
872C4×D4C22⋊D1112yes—
873C4×D4C22⋊D1111yescharacteristic
874C4×D4C22×D1111yescharacteristic
875C4×D4C22×D1112yes—
876C4×D4C22×D1111yescharacteristic
877C4×D4C22×D1112yes—
878C4×D4C22×D1111yescharacteristic
879#117—21no—
880#117—21no—
881#117—111no—
882#117—221no—
883#117C22×D1112yes—
884C2×C4⋊C4—221no—
885C2×C4⋊C4C22⋊D1111yescharacteristic
886C2×C4⋊C4C22×D1112yes—
887C2×C22⋊C4—22no—
888C2×C22⋊C4—22no—
889C2×C22⋊C4—222no—
890C2×C22⋊C4C22⋊D1112yes—
891C2×C42—221no—
892C2×C42C22×D1111yescharacteristic
893#107—111no—
894#107—112no—
895#107—111no—
896#106—112no—
897#106—111no—
898#106—111no—
899C4⋊C8—111no—
900C4⋊C8—111no—
901C4⋊C8—111no—
902C4⋊C8—111no—
903#103—111no—
904#103—111no—
905#103—111no—
906#103—112no—
907#103—112no—
908#103—112no—
909#103—111no—
910#103—112no—
911#103—112no—
912#102—111no—
913#102—112no—
914#102—112no—
915#102—111no—
916#102—111no—
917#102—112no—
918#102—112no—
919#102—112no—
920#102—111no—
921#102—112no—
922#102—112no—
923C22⋊C8—111no—
924C22⋊C8—111no—
925C22⋊C8—112no—
926C22⋊C8—112no—
927C22⋊C8—112no—
928C22⋊C8—112no—
929C22⋊C8—112no—
930C4×C8—112no—
931C4×C8—111no—
932C4×C8—111no—
933C2×C11—24no—
934C2×C11—42no—
935C2×C11—41no—
936C2×C11—82no—
937C2×C11—81no—
938C2×C11#348411yescharacteristic
939C2×C11C22×#13511yescharacteristic
940C2×C11#358511yescharacteristic
941D11—42no—
942D11—82no—
943C24—22no—
944C24—222no—
945C24C2×C22⋊D1112yes—
946#41—42no—
947#41—42no—
948#41—82no—
949#41—222no—
950#41—222no—
951#41—224no—
952#41—224no—
953#41—442no—
954#41—442no—
955#41—442no—
956#41—442no—
957#41—448no—
958#41—448no—
959C2×Q8—21no—
960C2×Q8—111no—
961C2×Q8—112no—
962C2×Q8—224no—
963C2×Q8—222no—
964C2×Q8—442no—
965C2×Q8C23×D1111yescharacteristic
966C2×D4—24no—
967C2×D4—22no—
968C2×D4—22no—
969C2×D4—21no—
970C2×D4—22no—
971C2×D4—22no—
972C2×D4—22no—
973C2×D4—21no—
974C2×D4—21no—
975C2×D4—22no—
976C2×D4—42no—
977C2×D4—42no—
978C2×D4—44no—
979C2×D4—84no—
980C2×D4—111no—
981C2×D4—112no—
982C2×D4—224no—
983C2×D4—221no—
984C2×D4—222no—
985C2×D4—222no—
986C2×D4—222no—
987C2×D4—222no—
988C2×D4—222no—
989C2×D4—221no—
990C2×D4—222no—
991C2×D4—221no—
992C2×D4—442no—
993C2×D4—448no—
994C2×D4—444no—
995C2×D4C2×C22⋊D1112yes—
996C2×D4C2×C22⋊D1111yescharacteristic
997C2×D4C2×C22⋊D1111yescharacteristic
998C2×D4C23×D1111yescharacteristic
999C2×D4C23×D1112yes—
1000C22×C4—22no—
1001C22×C4—21no—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—221no—
1007C22×C4—222no—
1008C22×C4—221no—
1009C22×C4—222no—
1010C22×C4—222no—
1011C22×C4—222no—
1012C22×C4—221no—
1013C22×C4—448no—
1014C22×C4C2×C22⋊D1111yescharacteristic
1015C22×C4C2×C22⋊D1111yescharacteristic
1016C22×C4C2×C22⋊D1112yes—
1017C22×C4C2×C22⋊D1112yes—
1018C22×C4C2×C22⋊D1112yes—
1019C22×C4C23×D1111yescharacteristic
1020C22×C4C23×D1112yes—
1021C22×C4C23×D1112yes—
1022Q16—222no—
1023Q16—442no—
1024SD16—222no—
1025SD16—224no—
1026SD16—222no—
1027SD16—442no—
1028SD16—442no—
1029SD16—442no—
1030SD16—442no—
1031D8—222no—
1032D8—224no—
1033D8—442no—
1034D8—442no—
1035D8—442no—
1036C2×C8—112no—
1037C2×C8—111no—
1038C2×C8—111no—
1039C2×C8—112no—
1040C2×C8—111no—
1041C2×C8—111no—
1042C2×C8—442no—
1043C2×C8—442no—
1044C2×C8—442no—
1045C2×C8—442no—
1046C4⋊C4—22no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—22no—
1052C4⋊C4—21no—
1053C4⋊C4—111no—
1054C4⋊C4—111no—
1055C4⋊C4—221no—
1056C4⋊C4—222no—
1057C4⋊C4—221no—
1058C4⋊C4—221no—
1059C4⋊C4—222no—
1060C4⋊C4—221no—
1061C4⋊C4C2×C22⋊D1111yescharacteristic
1062C4⋊C4C2×C22⋊D1111yescharacteristic
1063C4⋊C4C2×C22⋊D1112yes—
1064C4⋊C4C23×D1111yescharacteristic
1065C4⋊C4C23×D1112yes—
1066C4⋊C4C23×D1111yescharacteristic
1067C22⋊C4—22no—
1068C22⋊C4—22no—
1069C22⋊C4—21no—
1070C22⋊C4—21no—
1071C22⋊C4—21no—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—21no—
1076C22⋊C4—22no—
1077C22⋊C4—21no—
1078C22⋊C4—22no—
1079C22⋊C4—222no—
1080C22⋊C4—221no—
1081C22⋊C4—222no—
1082C22⋊C4—222no—
1083C22⋊C4—222no—
1084C22⋊C4—221no—
1085C22⋊C4—221no—
1086C22⋊C4—222no—
1087C22⋊C4—222no—
1088C22⋊C4C2×C22⋊D1112yes—
1089C22⋊C4C2×C22⋊D1112yes—
1090C22⋊C4C2×C22⋊D1112yes—
1091C22⋊C4C2×C22⋊D1112yes—
1092C42—22no—
1093C42—21no—
1094C42—221no—
1095C42—221no—
1096C42—221no—
1097C42C2×C22⋊D1111yescharacteristic
1098C42C2×C22⋊D1111yescharacteristic
1099C42C23×D1111yescharacteristic
1100C42C23×D1111yescharacteristic
1101C11#6156711yescharacteristic, complemented, Sylow
1102C23—24no—
1103C23—21no—
1104C23—22no—
1105C23—42no—
1106C23—42no—
1107C23—44no—
1108C23—82no—
1109C23—82no—
1110C23—221no—
1111C23—222no—
1112C23—444no—
1113C23—444no—
1114C23—882no—
1115C23C22×C22⋊D1112yes—
1116C23C22×C22⋊D1111yescharacteristic
1117C23C22×C22⋊D1112yes—
1118Q8—21no—
1119Q8—21no—
1120Q8—81no—
1121Q8—112no—
1122Q8—221no—
1123Q8—222no—
1124Q8—222no—
1125Q8—444no—
1126D4—24no—
1127D4—22no—
1128D4—21no—
1129D4—22no—
1130D4—22no—
1131D4—21no—
1132D4—42no—
1133D4—44no—
1134D4—44no—
1135D4—42no—
1136D4—82no—
1137D4—81no—
1138D4—82no—
1139D4—82no—
1140D4—82no—
1141D4—112no—
1142D4—224no—
1143D4—221no—
1144D4—222no—
1145D4—222no—
1146D4—444no—
1147D4—444no—
1148D4—444no—
1149D4—444no—
1150D4—444no—
1151D4—442no—
1152D4—881no—
1153D4—882no—
1154D4#6700314yescomplemented
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—82no—
1172C2×C4—82no—
1173C2×C4—82no—
1174C2×C4—224no—
1175C2×C4—221no—
1176C2×C4—221no—
1177C2×C4—221no—
1178C2×C4—222no—
1179C2×C4—444no—
1180C2×C4—444no—
1181C2×C4—444no—
1182C2×C4—444no—
1183C2×C4—442no—
1184C2×C4—881no—
1185C2×C4C22×C22⋊D1112yes—
1186C2×C4C22×C22⋊D1111yescharacteristic
1187C2×C4C22×C22⋊D1111yescharacteristic
1188C2×C4C22×C22⋊D1111yescharacteristic
1189C2×C4C22×C22⋊D1111yescharacteristic
1190C2×C4C22×C22⋊D1112yes—
1191C2×C4C22×C22⋊D1111yescharacteristic
1192C2×C4C24×D1111yescharacteristic
1193C8—221no—
1194C8—222no—
1195C8—221no—
1196C8—221no—
1197C8—221no—
1198C8—222no—
1199C22—22no—
1200C22—22no—
1201C22—21no—
1202C22—22no—
1203C22—21no—
1204C22—22no—
1205C22—21no—
1206C22—22no—
1207C22—42no—
1208C22—41no—
1209C22—42no—
1210C22—41no—
1211C22—41no—
1212C22—42no—
1213C22—84no—
1214C22—164no—
1215C22—222no—
1216C22—441no—
1217C22—441no—
1218C22—442no—
1219C22—442no—
1220C22—442no—
1221C22—888no—
1222C22C2×#6700314yes—
1223C22C23×C22⋊D1111yescharacteristic
1224C4—21no—
1225C4—21no—
1226C4—21no—
1227C4—22no—
1228C4—22no—
1229C4—21no—
1230C4—41no—
1231C4—42no—
1232C4—41no—
1233C4—41no—
1234C4—222no—
1235C4—441no—
1236C4—442no—
1237C4—441no—
1238C4C2×#6700312yes—
1239C4D11×H(5,𝔽2)11yescharacteristic
1240C4D11×H(5,𝔽2)11yescharacteristic
1241C2—24no—
1242C2—41no—
1243C2—42no—
1244C2—81no—
1245C2—82no—
1246C2—442no—
1247C2—882no—
1248C2#1308224711yescharacteristic
1249C2C22×#6700311yescharacteristic
1250C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3519C2
socleC22×C11C23×D4
hypercenter#3519D11
hypocenterC11#61567
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3519

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. D4×#4339C2semidirect
2. #13080560C2semidirect
3. #13080538C2semidirect
4. #13080512C2semidirect
5. #13080486C2semidirect
6. #13080460C2semidirect
7. #13080434C2semidirect
8. #13080372C2semidirect
9. #13080346C2semidirect
10. #13080319C2semidirect
11. D4×#4324C2semidirect
12. #13080297C2semidirect
13. D4×#4323C2semidirect
14. #13079588C2semidirect
15. #13079545C2semidirect
16. #13079404C2semidirect
17. #13079381C2semidirect
18. #13078670C2semidirect
19. #13078628C2semidirect
20. #13077832C2semidirect
21. C2×#10622650C2semidirect
22. #13077640C2semidirect
23. C11×#3519C2semidirect
24. C22×#4339C22semidirect
25. C11×#555C22semidirect
28. C11×#553C22semidirect
29. C11×#550C22semidirect
31. C11×#546C22semidirect
36. C11×#532C22semidirect
37. C11×#529C22semidirect
38. C11×#525C22semidirect
39. C2×C11×#121C22semidirect
42. C2×#67003C22semidirect
43. C2×#67003C22semidirect
45. C22×#4324C22semidirect
46. C22×#4323C22semidirect
47. #10623322C22semidirect
48. #10623084C22semidirect
49. #10623083C22semidirect
50. #10623082C22semidirect
51. #10623081C22semidirect
59. #10623008C22semidirect
60. C4×#4339C22semidirect
61. #10622852C22semidirect
62. #10622851C22semidirect
63. #10622831C22semidirect
64. #10622830C22semidirect
65. C2×C22⋊(C11⋊C8)C22semidirect
66. C2×C22⋊(C11⋊C8)C22semidirect
67. #10622706C22semidirect
68. #10622704C22semidirect
69. #10622701C22semidirect
70. #10622697C22semidirect
71. #10622689C22semidirect
72. #10622688C22semidirect
73. #10622686C22semidirect
74. #10622685C22semidirect
75. #10622681C22semidirect
76. #10622679C22semidirect
77. #10622676C22semidirect
78. #10622672C22semidirect
79. #10622670C22semidirect
80. #10622667C22semidirect
81. #10622664C22semidirect
82. #10622663C22semidirect
83. #10622661C22semidirect
84. #10622660C22semidirect
85. #10622660C22semidirect
86. #10622659C22semidirect
87. #10622658C22semidirect
88. #10622654C22semidirect
89. #10622654C22semidirect
90. #10622654C22semidirect
91. #10622653C22semidirect
92. #10622651C22semidirect
93. #10622651C22semidirect
94. #10622651C22semidirect
96. #10622650C22semidirect
97. #10622650C22semidirect
98. #10622650C22semidirect
99. #10622650C22semidirect
100. #10622650C22semidirect
101. #10622650C22semidirect
102. #10622650C22semidirect
103. #10622650C22semidirect
104. #10622649C22semidirect
105. #10622648C22semidirect
106. #10622648C22semidirect
107. #10622644C22semidirect
108. C4×#4326C22semidirect
109. #10622640C22semidirect
110. C4×#4325C22semidirect
111. #10622632C22semidirect
112. C4×#4324C22semidirect
113. C4×#4324C22semidirect
114. #10622629C22semidirect
115. #10622629C22semidirect
116. #10622628C22semidirect
117. C4×#4323C22semidirect
118. C4×#4323C22semidirect
121. D4×C11⋊C8C22semidirect
122. D4×C11⋊C8C22semidirect
123. D4×C11⋊C8C22semidirect
124. D4×C11⋊C8C22semidirect
125. #10622616C22semidirect
126. #10622615C22semidirect
127. #10622615C22semidirect
128. #10622609C22semidirect
129. #10622583C22semidirect
130. C2×#66874C22semidirect
131. #10622581C22semidirect
132. C2×#66873C22semidirect
133. #10622538C22semidirect
134. #10622538C22semidirect
477. #3519D11semidirect
534. D4×C11#135semidirect
602. #555C2×D11semidirect
605. #553C2×D11semidirect
607. #550C2×D11semidirect
615. #546C2×D11semidirect
624. #532C2×D11semidirect
625. #529C2×D11semidirect
628. #525C2×D11semidirect
629. C2×#121C2×D11semidirect
1101. C11#61567semidirect
1154. D4#67003semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D4×#43392
#130805602
#130805382
#130805122
#130804862
#130804602
#130804342
#130803722
#130803462
#130803192
D4×#43242
#130802972
D4×#43232
#130795882
#130795452
#130794042
#130793812
#130786702
#130786282
#130778322
C2×#106226502
#130776402
C11×#35192
#6156711